被动式电液加载系统的变刚度自适应控制
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摘要
建立了被动式电液加载系统的数学模型,分析由位置扰动和系统自身结构引起的稳态误差,讨论了负载刚度和液压刚度在系统主要行程范围内变化对系统动态特性的影响。采用高阶系统跟随低阶参考模型的自适应控制方法,在选择二阶参考模型的固有频率时综合考虑了两方面的因素,既发挥了液压动力机构响应频率高的优势又确定了合理的频宽。运用Narendra稳定自适应控制理论设计自适应控制器,建立增广误差模型,选取Lyapunov能量函数并导出能使系统全局渐进稳定的自适应律。利用Simulink软件进行数值仿真,仿真结果表明,加入自适应控制器后,系统能稳定地跟随参考模型,两者误差快速收敛为零,并且系统在5组不同参数设置下的动态响应性能几乎一致,上升时间和调整时间分别为4.8ms和14.6ms,稳态误差仅为0.03%;同时,由速度为0.5m/s的位置扰动引起的系统误差最大仅为0.58kN并于35ms后消除。故本文设计的自适应控制器使被动式电液加载系统在变参数和位置扰动条件下的动态特性和精度得到大幅提升。
This paper developed the mathematical model of passive electro-hydraulic loading system,analyzed the steady-state error caused by position disturbance and system structure,and discussed the influence of load stiffness and hydraulic stiffness changing within the stroke range of the actuator on the system dynamic characteristics.The adaptive control method of higher-order system following lower-order reference model was adopted.Natural frequency of the second-order reference model was selected by considering synthetically two factors,i.e.,the high response frequency of the hydraulic actuator and the reasonable bandwidth.An adaptive controller was designed by using Narendra’s stable adaptive control theory.The augmented error model was established.On the basis of Lyapunov energy function,adaptive law was derived which could make the system globally asymptotically stable.The results of numerical simulations by Simulink software show that the system with adaptive controller can stably follow the reference model,and the error converges to zero quickly.In five different parameter settings,the system has almost the same dynamic response performances with the rise time and adjustment time being 4.8 ms and 14.6 ms,respectively,and the steady-state error being only 0.03%.The maximal system error caused by position disturbance with a velocity of 0.5 m/s is only 0.58 kN and is eliminated in 35 ms.So the dynamic characteristics and accuracy of passive electro-hydraulic loading system with variable parameters and position disturbance have been greatly improved by the designed adaptive controller.
This paper developed the mathematical model of passive electro-hydraulic loading system,analyzed the steady-state error caused by position disturbance and system structure,and discussed the influence of load stiffness and hydraulic stiffness changing within the stroke range of the actuator on the system dynamic characteristics.The adaptive control method of higher-order system following lower-order reference model was adopted.Natural frequency of the second-order reference model was selected by considering synthetically two factors,i.e.,the high response frequency of the hydraulic actuator and the reasonable bandwidth.An adaptive controller was designed by using Narendra’s stable adaptive control theory.The augmented error model was established.On the basis of Lyapunov energy function,adaptive law was derived which could make the system globally asymptotically stable.The results of numerical simulations by Simulink software show that the system with adaptive controller can stably follow the reference model,and the error converges to zero quickly.In five different parameter settings,the system has almost the same dynamic response performances with the rise time and adjustment time being 4.8 ms and 14.6 ms,respectively,and the steady-state error being only 0.03%.The maximal system error caused by position disturbance with a velocity of 0.5 m/s is only 0.58 kN and is eliminated in 35 ms.So the dynamic characteristics and accuracy of passive electro-hydraulic loading system with variable parameters and position disturbance have been greatly improved by the designed adaptive controller.
引文
[1]田巨,王舰.电液负载模拟器现代控制策略研究[J].中国民航飞行学院学报,2014,25(6):49-53.
[2]苏世杰,游有鹏,齐继阳,等.电液伺服试验机力控系统负载刚度自适应控制[J].控制理论与应用,2018,35(4):429-437.
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[4]廖辉,尚晓新,蔡业彬,等.基于模型参考自适应控制的钻压控制的研究[J].液压与气动,2012(12):7-10.
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[7]张明伟,金晓宏,陶平,等.位置扰动型电液力控制系统多余力的抑制[J].武汉科技大学学报,2018,41(2):140-146.
[8]金晓宏,艾亚辉,黄浩,等.伺服阀滑阀阀口系数影响因素分析[J].武汉科技大学学报,2015,38(3):179-182.
[9]王春行.液压控制系统[M].北京:机械工业出版社,1999:137-139.
[10]吴忠强.两种跟踪低阶模型的模型参考自适应控制方案设计与仿真[J].系统仿真学报,2002,14(1):116-118.
[11]焦宗夏,华清,王晓东,等.负载模拟器的评价指标体系[J].机械工程学报,2002,38(11):26-30.
[12]李尚义,王宣银,岳继光,等.电液速度伺服系统-3dB频宽、穿越频宽、-10°频宽、-90°频宽的理论分析[J].机床与液压,1995(5):263-265.
[13]Narendra K S,Valavani L S.A comparison of Lyapunov and hyperstability approaches to adaptive control of continuous systems[J].IEEE Transactions on Automatic Control,1980,25(2):243-247.
[14]Jin Xiaohong,Rong Zhijun.Research on the adaptive model for electro-hydraulic position servo system with the external disturbances[C]//Proceedings of the Fourth International Symposium on Fluid Power Transmission and Control(ISFP’2003).Beijing:International Academic Publishers,World Publishing Corporation,2003,3:198-201.
[2]苏世杰,游有鹏,齐继阳,等.电液伺服试验机力控系统负载刚度自适应控制[J].控制理论与应用,2018,35(4):429-437.
[3]税洋,尉建利,闫杰.基于模型参考自适应控制的舵机加载系统研究[J].西北工业大学学报,2018,36(2):246-251.
[4]廖辉,尚晓新,蔡业彬,等.基于模型参考自适应控制的钻压控制的研究[J].液压与气动,2012(12):7-10.
[5]杨俭.液压压力机模型参考自适应控制系统的研究[J].机床与液压,2009,37(6):83-85.
[6]程校.负载中含负值弹性刚度电液伺服力加载系统的研究[D].武汉:武汉科技大学,2018:12-14.
[7]张明伟,金晓宏,陶平,等.位置扰动型电液力控制系统多余力的抑制[J].武汉科技大学学报,2018,41(2):140-146.
[8]金晓宏,艾亚辉,黄浩,等.伺服阀滑阀阀口系数影响因素分析[J].武汉科技大学学报,2015,38(3):179-182.
[9]王春行.液压控制系统[M].北京:机械工业出版社,1999:137-139.
[10]吴忠强.两种跟踪低阶模型的模型参考自适应控制方案设计与仿真[J].系统仿真学报,2002,14(1):116-118.
[11]焦宗夏,华清,王晓东,等.负载模拟器的评价指标体系[J].机械工程学报,2002,38(11):26-30.
[12]李尚义,王宣银,岳继光,等.电液速度伺服系统-3dB频宽、穿越频宽、-10°频宽、-90°频宽的理论分析[J].机床与液压,1995(5):263-265.
[13]Narendra K S,Valavani L S.A comparison of Lyapunov and hyperstability approaches to adaptive control of continuous systems[J].IEEE Transactions on Automatic Control,1980,25(2):243-247.
[14]Jin Xiaohong,Rong Zhijun.Research on the adaptive model for electro-hydraulic position servo system with the external disturbances[C]//Proceedings of the Fourth International Symposium on Fluid Power Transmission and Control(ISFP’2003).Beijing:International Academic Publishers,World Publishing Corporation,2003,3:198-201.